Millersville University
Department of Mathematics
MATH 161, Calculus I, Limits
Examples
1. Use the graph of f(x) show below to find the following limits. If a limit does not exist,
be prepared to explain why.
-4 -2 0 2 4
x
-0.5
0
0.5
1
1.5
2
y
(a) lim
x→−2−
f(x)
(b) lim
x→−2+f(x)
(c) lim
x→−2f(x)
(d) lim
x→0f(x)
(e) lim
x→2+f(x)
2. Evaluate the following limits, if they exist. If a limit does not exist, be prepared to
explain why.
(a) lim
x→3+(x+ 2)(3x−1)
(b) lim
x→−3
x2−x+ 12
x+ 3
(c) lim
x→9−
9−x
3−√x
(d) lim
x→2
1
x−1
2
x−2
(e) lim
x→2|x−2|
x−2